Near time-optimal jerk trajectory for positioning a control object

ABSTRACT

Method and apparatus for control object manipulation from an initial position to a final position. A jerk control profile describes a near time-optimal jerk trajectory for the control object and includes a sequence of first, second and third sinusoidal pulses of respectively alternating polarity and common absolute magnitude. The area of the second pulse is nominally equal to the combined area of the first and third pulses, and the pulses are preferably symmetric about the respective maximum pulse values. Associated control profiles (control voltage, current, velocity, displacement, etc.) are derived from the jerk control profile. For longer seeks, constant, non-zero jerk segments are inserted into the profile between the pulses, during which control voltage is maintained near saturation. The control object preferably comprises a transducer in a data storage device and the jerk control profile is stored in a memory location of the device.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Grant No.CMS-9978748 awarded by the National Science Foundation. The governmenthas certain rights in the invention.

FIELD OF THE INVENTION

The claimed invention relates generally to the field of control systemsand more particularly, but not by way of limitation, to an apparatus andmethod for moving a control object from an initial position to a finalposition using a near time-optimal jerk trajectory.

BACKGROUND

Control systems are used to move a variety of control objects from aninitial position to a final position. For example, data storage devicescommonly utilize a closed loop servo control system to position a datatransducer adjacent individual tracks on a data storage medium.

A well known servo control approach is Pontryagin's Time-Optimal ControlSolution, which generally operates to change the system state in minimumtime while at all times using all available system power. This approachis sometimes also referred to as Bang-Bang Control.

While time-optimal, some real world applications can limit the viabilityof this approach due to the presence of variable or unquantifiablesystem resonances. More particularly, abrupt changes in jerk (change inacceleration with respect to time) can serve as a broad spectrumexcitation of the system, resulting in unacceptably long settle times atthe final position.

Accordingly, there is a continual need for improvements in the manner inwhich control trajectories are formulated as part of a control solution,such as but not limited to the controlled movement of a transducer in adata storage device.

SUMMARY OF THE INVENTION

Preferred embodiments of the present invention are generally directed toan apparatus and method for moving a control object from an initialposition to a final position, such as a transducer in a data storagedevice.

A jerk control profile is provided to describe a near time-optimal jerktrajectory for the control object. The jerk control profile comprises asequence of first, second and third sinusoidal pulses of respectivelyalternating polarity and common absolute magnitude. The area of thesecond pulse is nominally equal to the combined area of the first andthird pulses, and the pulses are preferably symmetric about therespective maximum pulse values.

Associated control profiles (control voltage, current, velocity,displacement, etc.) are derived from the jerk control profile. Forlonger seeks, constant, non-zero jerk segments are inserted into theprofile between the pulses, during which control voltage is maintainednear saturation.

These and various other features and advantages which characterize theclaimed invention will become apparent upon reading the followingdetailed description and upon reviewing the associated drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exploded view of a data storage device constructed andoperated in accordance with preferred embodiments of the presentinvention.

FIG. 2 is a generalized functional block diagram of the device of FIG. 1in conjunction with a host.

FIG. 3 provides magnitude and phase bode plot representations of systemresonances of the device of FIG. 1.

FIG. 4 is a functional block representation of relevant portions of aservo control circuit of the device constructed and operated inaccordance with preferred embodiments to control the position oftransducers of the device in view of the system resonances referenced inFIG. 3.

FIG. 5 provides a graphical representation of a segmented, three pulsejerk profile for short seeks by the device.

FIG. 6 denotes the relationship between maximum jerk magnitude and seektime.

FIG. 7 sets forth a family of control profiles derived from the shortseek jerk profile of FIG. 5.

FIG. 8 illustrates the relationship between seek time and seek lengthusing the jerk profile of FIG. 5.

FIG. 9 provides a graphical representation of a segmented, three pulsejerk profile for long seeks by the device.

FIG. 10 sets forth a family of control profiles derived from the longseek jerk profile of FIG. 9.

FIG. 11 is a flow chart for a PROFILE GENERATION routine, illustrativeof steps carried out in accordance with preferred embodiments of thepresent invention.

DETAILED DESCRIPTION

To illustrate an exemplary environment in which presently preferredembodiments of the present invention can be advantageously practiced,FIG. 1 shows an exploded view of a data storage device 100. The device100 is preferably characterized as a small form factor disc drive usedto store and retrieve user data in a battery-operated, handheld mobileproduct such as a notebook computer or a digital camera, but such is notlimiting to the scope of the claimed subject matter.

The device 100 includes a rigid, environmentally controlled housing 101formed from a base deck 102 and a top cover 104. A spindle motor 108 ismounted within the housing 101 to rotate a number of data storage media110 (in this case, two) at a relatively high speed.

Data are stored on the media 110 in an array of concentric tracks (notshown), having a nominal radial density of about 100K tracks/inch (in).The tracks are accessed by a corresponding array of data transducingheads 112 (transducers). The heads 112 are supported by an actuator 114and moved across the media surfaces by application of current to a voicecoil motor, VCM 116. A flex circuit assembly 118 facilitatescommunication between the actuator 114 and control circuitry on anexternally mounted printed circuit board, PCB 120.

As shown in FIG. 2, the control circuitry preferably includes aninterface circuit 124 which communicates with a host device 126 using asuitable interface protocol (fibre channel, SAS, SCSI, etc.). Theinterface circuit 124 includes a buffer (cache memory) 128 for thetemporary storage of data being transferred to or from the media 110. Acontroller 130 provides top level control for the device 100 and ispreferably characterized as a programmable, general purpose processorwith suitable programming to direct the operation of the device 100.

A read/write channel 132 encodes data to be written to the media 110during a write operation and reconstructs transduced readback signalsfrom the media 110 to reconstruct previously stored data during a readoperation. A preamplifier/driver circuit (preamp) 134 provides headselection circuitry and conditions signals provided to and received fromthe heads 112.

A servo circuit 136 provides closed loop positional control for theheads 112. The servo circuit 136 preferably includes a digital signalprocessor (DSP) 138 which operates in accordance with associatedprogramming and data in memory (MEM) 139 and in response to controlinputs from the top level controller 130. A two processor system ispreferred, but not required.

During a seek operation, the servo circuit 136 moves a selected head 112from an initial track to a destination track on the associated mediasurface. Generally, the seek operation is not concluded until the headhas successfully settled onto the destination track and the servocircuit is able to follow that track to allow the initiation of dataaccess operations therewith.

It is desirable to carry out seeks in a minimum amount of time in orderto maximize overall data throughput rates with the host 126. However,system resonances can adversely impact seek times, since the undesiredexcitation of such resonances during the movement of the actuator 114can lengthen the settling time as the head 112 oscillates about thedestination track.

FIG. 3 provides magnitude and phase bode plots 140, 142 ofrepresentative resonance responses of the device 100. System resonancescan arise from a number of factors, including flexible modes of theactuator arms, bearing translation modes, disc flutter, and windageeffects. These resonances are not easily modeled and can vary over timeand under different environmental conditions.

FIG. 4 provides a functional block representation of relevant portionsof the servo control circuit 136. Portions of the circuitry of FIG. 4are preferably embodied in programming executed by the DSP 138. While anapplied voltage approach has been employed, this is merely for purposesof providing a concrete example and is not limiting.

A feed forward trajectory generator 144 derives and supplies controlprofiles to govern the execution of each seek. A control voltage (V_(C))is supplied via path 146 to a summing junction 148. The output of thesumming junction 148, applied voltage (V_(A)), is provided to the VCM116 via path 149. Coil inductance of the VCM 116 is depicted at block150, and provides a current (I) output on path 152. Derivation block 154is used to take the derivative of current (dI/dt) to provide anindication of jerk (J) on path 156.

Block 158 represents system gain (K_(s)). A system resonance transferfunction (TF) is denoted at block 160 to represent the effects of theresonances of FIG. 3. The output of block 160 is an acceleration (A)signal (path 162), which is integrated (1/s) by block 164 to providevelocity (VEL) on path 166.

Integrator 168 integrates velocity to provide an indication of position(X) on path 170. A back electromotive force (bemf) gain block (K_(B))172 scales the velocity for input back to the summing junction 148. Thefeed forward trajectory generator utilizes the various outputs of thecircuitry (position, velocity, etc.) to adjust the operation of thecircuit to bring the head 112 to the destination track, depending uponthe control mode (velocity control, position control, model reference,etc.).

It can be seen at this point that if the feed forward trajectorygenerator 144 were to utilize a time-optimal control voltage profile(e.g., square wave pulses to accelerate and then decelerate the head112), the associated large changes in jerk would cause significantexcitation of the system resonances (block 160). This was confirmed bycomputer simulations which found that overall seek time for a particularseek increased from an ideal seek time of about 3 milliseconds, ms toaround 25 ms due to excessive oscillation during settling.

Accordingly, preferred embodiments of the present invention generallyoperate to provide a near time-optimal solution. A near time-optimalsolution is defined herein as a feed-forward trajectory that can beshown to be comparable to the performance of a time-optimal solution fora simpler ideal model, and that incorporates some method of vibrationminimization or disturbance rejection for phenomena that cannot beadequately modeled.

A short seek jerk trajectory is first set forth by a jerk profile 180 inFIG. 5. This trajectory satisfies a position constraint such thatconstraints on a maximum allowable velocity and a maximum allowablecontrol voltage are not met during the seek. The trajectory further endsthe seek with zero velocity and zero acceleration or current.

As shown in FIG. 5, the profile 180 is a segmented, three pulse jerkprofile with first, second and third pulses 182, 184, 186. The pulsesare preferably sinusoids as a function of time T. The first and thirdpulses 182, 186 are of a first polarity (e.g., positive) and the secondpulse 184 is of opposite polarity (e.g., negative). As those skilled inthe art will recognize, the respective polarities depend on thedirection of travel of the control object.

All three pulses 182, 184, 186 have the same absolute maximum magnitude(a maximum jerk, J_(M)), and the combined pulse widths of the first andthird pulses 182, 186 (each 1T) are set equal to the pulse width of thesecond pulse 184 (2T). Thus, the combined areas of the first and thirdpulses are equal to the second pulse, which satisfies the endingrequirement of zero velocity and acceleration/current. Limiting theprofile to three pulses (as opposed to incorporating additional pulses)has been found to advantageously limit excitation of the systemresonances.

The short seek profile 180 of FIG. 5 thus has a baseline seek time of4T, which can be adapted for individual seek lengths. Optimization fordifferent seek lengths can be carried out using well known numericalmethods, such as optimization routines from Matlab® software, TheMathworks, Inc., Natick, Mass., USA.

The pulses 182, 184, 186 are preferably first order sine functionsegments, although other curvilinear waveforms can be utilized as wellincluding modified 1-cosine functions to provide improved transitionbetween segments. An advantage of using a sinusoid based waveform is areduction in the excitation of the system resonances.

This advantage is further realized through the use of substantiallysymmetric pulses, as shown in FIG. 5. That is, each of the first,second, and third pulses 182, 184, 186 can be seen to comprise a leadingportion that approaches a maximum value of the pulse (J_(M) or −J_(M))and a trailing portion that extends away from the maximum value of thepulse. In each case, the leading portion is nominally identical to thetrailing portion so that the pulses are nominally symmetric about theassociated maximum value.

The individual values from the profile 180 can be calculated on the fly,but are preferably stored as a discrete series of baseline values in atable. A dedicated table can be established in DSP memory 139 (FIG. 2)to provide all of the values set forth in FIG. 5 (from 0 to 4T).Alternatively, a utility sine table such as accessible to bothcontroller 130 and DSP 138 can be accessed and segmented to provide the0 to 1T, 1T to 3T and 3T to 4T pulses.

It will be noted that the profile 180 of FIG. 5 is generally only afunction of one variable, the maximum allowable value of jerk (J_(M)).This value can be selected analytically, such as through finite elementmodeling of the actuator, or empirically, such as shown by FIG. 6.

FIG. 6 provides a maximum jerk versus seek time curve 188, whichgenerally illustrates that within controllable ranges, higher values ofJ_(M) generally provides shorter seek times (for a given seek length),but the rate of return varies. It was found in one example that anincrease in J_(M) from 2,000 in/s³ to 4,000 in/s³ resulted in a seektime decrease of 1.75 ms, but an increase in J_(M) from 8,000 in/s³ to10,000 in/s³ resulted in a seek time decrease of less than 0.5 ms.

By selecting appropriate weighting factors on seek time and maximumallowable jerk, a relationship such as curve 188 can be utilized toself-tune a maximum allowable jerk value.

The short seek jerk profile 180 is used to generate other controlprofiles such as exemplified in FIG. 7, including control voltageprofile 190, current profile 192, velocity profile 194 and position(displacement) profile 196. As will be recognized, integrating jerkprovides current, integrating current provides velocity, and integratingvelocity provides position. Referring again to FIG. 4, the relationshipbetween control voltage V_(C)and current I can be set forth as:V _(A) =V _(C) −V _(B)  (1)V _(C) =V _(A) +V _(B)=L(dI/dt)+I(R)+V _(B)=L(J)+I(R)+K_(B)(VEL)where L is the inductance of the coil, R is the resistance of the coil.Preferably, the requisite control profiles are generated by the feedforward trajectory generator 144 from the short seek jerk profile 180for each seek, and scaled to the appropriate seek length. This has beenfound to be an advantageous solution since the profile is preferably afunction of only one variable (max jerk J_(M)), allowing the requisitecalculations to be generated in a resource efficient manner. Empiricalanalysis has shown that the resulting profile 180 provides seek timesthat are comparable to ideal time-optimal seeks and that significantexcitations of system resonances are avoided, so that the profile meetsthe near time-optimal formulation set forth above.

As mentioned previously, the short seek profile 180 meets constraints onmaximum velocity and maximum control voltage. The maximum velocityconstraint is a design criterion that specifies the maximum allowablevelocity of the head 112 to prevent damage to the device 100 in theevent of a run-away condition in which the actuator slams at full speedinto an end-of-stroke limit stop. The maximum control voltage representssaturation of the power amplifier that supplies voltage and current tothe coil.

The maximum seek length that can be carried out using the short seekprofile 180 is thus that length of seek at which the first of thesecriteria is met. FIG. 8 provides a curve 198 that illustrates seek timev. seek length results for a selected value of J_(M). Empirically it wasdetermined in one example that short seeks could be extended to14,429.25 tracks before the control voltage constraint was violated (thevelocity constraint was never violated over this interval).

It is contemplated that short seeks constitute the majority of seekaccess events during normal operation of data storage devices such as100. Thus, in some preferred embodiments a profile such as 180 isutilized to control shorter seeks, and longer seeks are carried outusing conventional velocity control or other methodologies.

Alternatively, a long seek jerk trajectory can be utilized based on theshort seek profile 180 of FIG. 5. This long seek trajectory shouldsatisfy a position constraint such that the constraints on the maximumallowable velocity and maximum allowable control voltage are met for aslong as possible, but not violated. Because the control voltage will bemaintained near, but not surpassing saturation, the pulses from theprofile 180 should not be widened.

Accordingly, a long seek jerk profile 200 is set forth by FIG. 9. Theoverall time scale remains at 4T, but it will be understood that first,second and third pulses 202, 204, 206 are nominally identical to thepulses 182, 184, 186 in FIG. 5.

Equal and opposite constant jerk segments 208, 210 are respectivelyinserted between the first and second pulses 202, 204 and between thesecond and third pulses 204, 206 as shown. These constant jerk segments208, 210 are preferably non-zero to account for the effects of bemfvoltage (V_(B)), and to enhance control effort.

Those skilled in the art can empirically select appropriate levels forthe segments 208, 210; in one example the magnitudes of these segments208, 210 was set at ±212.5 in/s³ based on an optimization analysis. Itwill be noted that using equal and opposite segments further maintainsthe “balance” of the area above the zero line with the area below thezero line in the profile, maintaining the end seek constraints of zerovelocity and zero current/acceleration. The lengths of the segments 208,210 are not fixed, but rather extended or contracted as required inrelation to the length of the long seek.

Associated control profiles from the long seek profile 200 areexemplified in FIG. 10 to include control voltage profile 212, currentprofile 214, velocity profile 216 and position (displacement) profile218. These profiles are utilized as desired to carry out a long seek;for example, a velocity control approach may be performed whereby thecontrol object (head 112) is caused to follow the velocity trajectory ofprofile 216.

As before, empirical studies have shown that the long seek profile 200provides seek times that are comparable to the ideal time-optimalsolution discussed above, with significant disturbance rejection ascompared to the time-optimal solution.

A small amount of localized shaping (e.g., radiusing) can be applied tothe respective ends of the segments 208, 210 as desired to smooth outthe abrupt “corners” in FIG. 9, thereby further reducing the prevalenceof abrupt changes in jerk that might excite the system resonances duringlong seeks. Such shaping still maintains balance of the profile and ispreferably restricted to a relatively few sample points at the ends ofthe constant-jerk segments 208, 210.

FIG. 11 sets forth a flow chart for a PROFILE GENERATION routine 300 tosummarize steps preferably carried out in accordance with preferredembodiments of the present invention for a data storage device such as100 or other control system.

A maximum allowable jerk value J_(M) is identified at step 302 usinganalytical or empirical techniques, as discussed above. Next, asegmented, three pulse jerk profile is formulated such as exemplified byprofile 180 in FIG. 5, with the profile pulses preferably characterizedas sinusoids at the maximum jerk J_(M) and balanced pulse widths tosatisfy the end seek constraints.

At step 306, the maximum short seek length is determined by extendingseek lengths until at least one of a maximum velocity and a maximumvoltage constraint are met. A long seek jerk profile is next formulatedat step 308 by utilizing equal and opposite, non-zero constant jerksegments between the pulses as set forth by the profile 200 in FIG. 9.As desired, shaping (radiusing) of the ends of the constant jerksegments is applied as discussed previously.

Associated control profiles are next preferably derived from therespective base jerk profiles 180, 200 at step 310, as shown in FIGS. 7and 10. The control profiles are thereafter utilized to carry out seekoperations to move the control object from a first position to a finalposition at step 312, and the routine ends at step 314.

For purposes of the appended claims, the phrase near “time-optimal” willbe defined consistent with the foregoing discussion as a trajectory thatprovides seek times comparable to an ideal time-optimal (bang-bang)solution and that includes a characteristic to reduce excitation ofsystem resonances. The recited “area” of a pulse will be defined as thatarea bounded by the pulse and a mid-line extending between the maximumvalue of the pulse and the maximum value of another pulse in thesequence of opposite polarity (such as the mid-line “0” in FIGS. 5 and9). The term “sinusoidal” will be defined broadly to include waveformsthat substantially resemble first order sinusoidal pulses, and includes,but is not limited to, first order sinusoids, modified 1-cosinesinusoids, multi-order curvilinear (parabolic) functions, etc.

The recited “first means” will be understood to correspond to thedisclosed DSP 138 with associated DSP memory 139, which operates to setforth the circuitry of FIG. 4 in accordance with one or both of therespective three-pulse jerk profiles 150, 200 of FIGS. 5 and 9. Jerkprofiles with more than three pulses, and jerk profiles with pulses thatare not nominally symmetric (both in total about the mid-line andindividually about the pulse maximum magnitudes) are excluded from thedefinition of an equivalent.

It is to be understood that even though numerous characteristics andadvantages of various embodiments of the present invention have been setforth in the foregoing description, together with details of thestructure and function of various embodiments of the invention, thisdetailed description is illustrative only, and changes may be made indetail, especially in matters of structure and arrangements of partswithin the principles of the present invention to the full extentindicated by the broad general meaning of the terms in which theappended claims are expressed. For example, the particular elements mayvary depending on the particular control environment without departingfrom the spirit and scope of the present invention.

In addition, although the embodiments described herein are directed to adata storage device that employs a closed loop servo control circuit tomove a transducer adjacent a data storage medium, it will be appreciatedby those skilled in the art that the claimed subject matter is not solimited and various other control object positioning systems, includingany number of automated robotic actuator or positioning systems thatemploy rotational, linear or multi-axis motion, can be utilized withoutdeparting from the spirit and scope of the claimed invention.

1. A method comprising a step of moving a control object from an initialposition to a final position using a near time-optimal jerk controlprofile comprising a sequence of first, second and third sinusoidalpulses of respectively alternating polarity and common absolutemagnitude, the area of the second pulse selected to be nominally equalto the combined area of the first and third pulses, wherein each of thefirst, second, and third pulses comprises a leading portion thatapproaches a maximum value of the pulse and a trailing portion thatextends away from the maximum value of the pulse, and wherein theleading portion is nominally identical to the tailing portion so thateach said pulse is nominally symmetric about said maximum value, andwherein the jerk control profile further comprises a first constant,non-zero jerk segment between the first and second pulses and a secondconstant, non-zero jerk segment between the second and third pulses. 2.The method of claim 1, wherein each of the first, second, and thirdpulses comprises a sine function.
 3. The method of claim 1, furthercomprising a step of deriving at least a selected one of a controlvoltage profile, a current profile, a velocity profile and adisplacement profile to describe an associated characteristic trajectoryfor the control object from the jerk control profile.
 4. The method ofclaim 3, further comprising a step of utilizing the at least a selectedone of said control voltage profile, current profile, velocity profileand displacement profile to move the control object from the initialposition to the final position.
 5. The method of claim 1, wherein eachof the first, second, and third pulses comprises a cosine function. 6.The method of claim 1, wherein the first and second constant, non-zerojerk segments each share a common absolute magnitude.
 7. The method ofclaim 1, wherein the control object comprises a transducer in a datastorage device and wherein the method further comprises storing the jerkcontrol profile in a memory location of said device.
 8. A methodcomprising a step of moving a control object from an initial position toa final position in accordance with a jerk control profile thatdescribes a near time-optimal jerk trajectory for the control object,the jerk control profile comprising a first sinusoidal pulse of firstpolarity, a second sinusoidal pulse of second polarity opposite thefirst polarity and a third sinusoidal pulse of first polarity, whereinthe second sinusoidal pulse comprises an area equal to a combined areaof the first and third sinusoidal pulses, and wherein the jerk controlprofile further comprises a first constant, non-zero jerk segmentbetween the first and second pulses and a second constant, non-zero jerksegment between the second and third pulses.
 9. The method of claim 8,wherein each of the first, second and third pulses peak at a commonmaximum absolute magnitude, wherein each of the first, second and thirdpulses has a leading portion that approaches said absolute magnitude anda trailing portion that extends away from said absolute magnitude, andwherein the first and second portion are substantially symmetric withrespect to said absolute magnitude.
 10. The method of claim 8, furthercomprising a step of deriving at least a selected one of a controlvoltage profile, a current profile, a velocity profile and adisplacement profile to describe an associated characteristic trajectoryfor the control object from the jerk control profile.
 11. The method ofclaim 10, wherein the moving step comprises utilizing the at least aselected one of said control voltage profile, current profile, velocityprofile and displacement profile to move the control object from theinitial position to the final position.
 12. The method of claim 8,further comprising steps of selecting a maximum jerk value and settingthe respective maximum magnitudes of the first, second and third pulsesequal to said maximum jerk value.
 13. The method of claim 8, whereineach of the first, second, and third pulses comprises at least aselected one of a sine or a cosine function.
 14. The method of claim 8,wherein the first and second constant, non-zero jerk segments each sharea common absolute magnitude.
 15. An apparatus comprising a controlobject and first means for moving the control object from an initialposition to a final position using a jerk control profile comprising asequence of first, second and third sinusoidal pulses of respectivelyalternating polarity and common absolute magnitude, the area of thesecond pulse selected to be nominally equal to the combined area of thefirst and third pulses, the jerk control profile further comprising aconstant non-zero jerk segment between the first and second sinusoidalpulses.
 16. The apparatus of claim 15, wherein the first means comprisesa feed-forward trajectory generator.
 17. The apparatus of claim 16,wherein the first means further comprises a memory in which the jerkcontrol profile is stored.
 18. The apparatus of claim 15, wherein thecontrol object comprises a transducer in a data storage device.